Chapter2b–(Transformationsof(Functions–(REVIEW( 1) c) d) e 2b... · Microsoft Word - Chapter 2b...
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Chapter 2b – Transformations of Functions – REVIEW MCR3U Jensen 1) List the transformations of, in words, of () for each of the following functions. a) = 2() b) ℎ = ( − 3) c) = ! ! d) = (−) e) = − 3 2) List the transformations, in words, of () for each of the following functions in the order you would do them in. a) = −( + 2) b) ℎ = 3 + 2 c) = 3(−) 3) List the transformations, in words, of = ! to = 3 − 2 ! − 11 in the order you would do them. 4) List the transformations, in words of = to = 2 ( − 3) − 9 in the order you would do them.
Transcript of Chapter2b–(Transformationsof(Functions–(REVIEW( 1) c) d) e 2b... · Microsoft Word - Chapter 2b...
Chapter 2b – Transformations of Functions – REVIEW MCR3U Jensen 1) List the transformations of, in words, of 𝑓(𝑥) for each of the following functions. a) 𝑔 𝑥 = 2𝑓(𝑥) b) ℎ 𝑥 = 𝑓(𝑥 − 3) c) 𝑗 𝑥 = 𝑓 !
!𝑥
d) 𝑘 𝑥 = 𝑓(−𝑥) e) 𝑚 𝑥 = 𝑓 𝑥 − 3 2) List the transformations, in words, of 𝑓(𝑥) for each of the following functions in the order you would do them in. a) 𝑔 𝑥 = −𝑓(𝑥 + 2) b) ℎ 𝑥 = 𝑓 3𝑥 + 2 c) 𝑗 𝑥 = 3𝑓(−𝑥) 3) List the transformations, in words, of 𝑓 𝑥 = 𝑥! to 𝑔 𝑥 = 3 𝑥 − 2 ! − 11 in the order you would do them. 4) List the transformations, in words of 𝑓 𝑥 = 𝑥 to 𝑔 𝑥 = 2 (𝑥 − 3)− 9 in the order you would do them.
5) Perform the following transformations on the graphs below.
a) translate up 2 units
b) horizontal stretch by a factor of 2 c) vertical compression by a factor of !
!
6) For the graph of f (x) given, sketch the graph of g(x) after the given transformation. List the transformations in words as well.
a) 𝑔 𝑥 = −𝑓(𝑥)
b) 𝑔 𝑥 = 𝑓(−𝑥)
−11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 11
−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
7
8
9
10
x
y
−11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 11
−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
7
8
9
10
x
y
7) For each function 𝑔(𝑥):
i) describe the transformations from the parent function 𝑓 𝑥 ii) create a table of values of image points for the transformed function iii) graph the parent function and the transformed function and write its equation
a) 𝑓 𝑥 = 𝑥!. Graph 𝑔 𝑥 = 2𝑓(𝑥 − 2). b) 𝑓 𝑥 = 𝑥. Graph 𝑔 𝑥 = −𝑓(2𝑥).
−11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 11
−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
7
8
9
10
x
y
c) 𝑓 𝑥 = 𝑥!. Graph 𝑔 𝑥 = 4𝑓(𝑥 − 3) d) 𝑓 𝑥 = 𝑥. Graph 𝑔 𝑥 = 3𝑓 −𝑥 − 2.
−11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 11
−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
7
8
9
10
x
y
−4 −3 −2 −1 1 2 3 4
−4
−3
−2
−1
1
2
3
4
x
ye) 𝑓 𝑥 = !
! . Graph 𝑔 𝑥 = 2𝑓 𝑥 − 1 + 0.5 (don’t graph parent function)
8) For each function 𝑔(𝑥):
i) determine the parent function and describe the transformations from the parent function 𝑓 𝑥 ii) create a table of values of image points for the transformed function iii) graph the parent function and the transformed function
a) 𝑔 𝑥 = −2 𝑥 + 2 ! + 4
−11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10 11
−11
−10
−9
−8
−7
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
7
8
9
10
x
y
−4 −3 −2 −1 1 2 3 4
−4
−3
−2
−1
1
2
3
4
x
y
b) 𝑔 𝑥 = −2 −4 𝑥 + 2 − 3 c) 𝑔 𝑥 = !!
!!(!!!.!)
+ 1 (don’t graph parent function)
9) Find the inverse , 𝑓!! 𝑥 , algebraically if 𝑓 𝑥 = −2 𝑥 + 1 − 5 10) Find the inverse , 𝑓!! 𝑥 , algebraically if 𝑓 𝑥 = !
!(𝑥 − 4)! + 2
Answers 1) a) vertical stretch BAFO 2 b) phase shift right 3 units c) horizontal stretch BAFO 3 d) horizontal reflection in the y-‐axis e) shift down 3 units 2) a) vertical reflection in the x-‐axis and then shift left 2 units. b) horizontal compression BAFO !
! and then shift up 2 units.
c) vertical stretch BAFO 3 and then horizontal reflection in the y-‐axis. 3) vertical stretch BAFO 3, then shift right 2 units and down 11 units. 4) vertical stretch by a factor of 2, then shift right 2 units and down 9 units. 5) a) b) c) 6) a) vertical reflection in the x-‐axis b) horizontal reflection in the y-‐axis See posted solutions for 7&8
9) 𝑓!! 𝑥 = !!!!!
!− 1
10) 𝑓!! 𝑥 = ± 3(𝑥 − 2)+ 4
